Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
574 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 574 conjugacy classes of subgroups — too many to draw. Only its 131 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20283796 | C2 | semidirect |
| 4. #20272616 | C2 | semidirect |
| 5. C53×#1801 | C2 | semidirect |
| 136. #1801 | D53 | semidirect |
| 159. C53 | #9398 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283796 | 2 |
| #20279714 | 2 |
| #20273384 | 2 |
| #20272616 | 2 |
| C53×#1801 | 2 |
| #9398 | 53 |